This document provides guided notes on solving word problems using matrices. It includes an example problem about the profits from different types of apples sold at different markets. It then explains how to set up the problem with value matrices A and B and that the solution matrix represents the profits for each market. Students are directed to complete similar problems on page 373. The document also covers calculating determinants for 2x2 and 3x3 square matrices, noting an easier pattern than memorizing the 3x3 formula.

1. Chapter 8.8 Guided Notes
Use page 372 and 373
Example Problem
An orchard grows Delicious, Jonathan, and Granny Smith apples. The apples are
sold in boxes to two different markets. The profit is $5.85 on a box of Delicious
apples, $4.25 on a box of Jonathan apples, and $3.75 on a box of Granny Smith
apples. Find the profit of each market.
What are the values in matrix A?
What are the values in matrix B?
What do the numbers in the solution matrix represent?
Use this process to complete numbers 1 – 3 on page 373. Be sure to set up your
matrices first, then use matrix multiplication to find your solution matrix.

2. Determinants
A matrix is a “square” matrix if it has the same number of rows and columns. For
example, a 2x2 matrix is a square matrix.
You can figure out the determinant of a 2x2 square matrix with the following
method:
Find the determinants of the following matrices:
You can figure out the determinant of a 3x3 square matrix with the following
formula:
Can you notice a pattern that is easier than memorizing the formula?
Find the determinants of the following matrices.